Construct chroniclesFor each fuzzy clusters of step ‚:

instances are sorted in the decreasing order of their membership degree

the T first instances that respect the Q criterion are retained to construct a chronicle.

Goal: extraction of temporal patterns that discriminate event sequences

• Long event sequences• Few event types• Numerical temporal information is of major

importance

Temporal patterns: chronicles Sets of events such that the delay between their occurrences is bounded by a numerical interval

A B[0,3]

A[-1,4]

B[0,3]

A [2,2]

C

B CBC A

Motivation Temporal Inductive Database

A B BC

Queries

Answers

Freq(C,L1) ¸ 5 Æ Freq(C,L2) · 8 Æ C v C1

Freq(C1,L) ¸ 10 Æ L 2 D …

Temporal patterns : Chronicles Data : Event sequences

Event sequences

Chronicles

B B BA B BA B BA B A B A B BA

Chronicle Recognition in Event Sequences

i1

i2

i3

i4

i5

i6

i7

i8

i9

i10

i11

Qe&d - The earliest distinct instances criterion Qe&d (C1,L1) = {i1, i8, i10}• Two instances have no common events • Instances occur as early as possible according to a total order on instances in the

sequence

Qm - The minimal occurrences criterion Qm(C1,L1) ={i1, i6, i8, i9, i10}

• An instance is not contained by another instance

Qd - The distinct instances criterion Qd (C1,L1) ={i2, i7, i8, i10}

• Selects instances that form a maximum clique in the graph of distinctness instances.

An Order Relation on Chronicles

B[-1,3]

[1,5]B[-3,-2]

A

B[-2,5]

A

B[1,2]

A C[1,2]

B[1,2]

[1,5]B[-3,-2]

A C[1,2]

L1:

Instances ofC1 in L1

L : An event sequence W : A maximal time window T : A minimum frequency threshold Q :A recognition criterion

(Application dependent)

Input

Find every frequent parallel episodes

Apriori manner

Format of every temporal constraints : [-W,W]

… AB

CA

BC

Fuzzy cluster instances of chronicles found in step .

Instances of the chronicle C2

C2

Compute the set of the frequent minimal (maximally specific) chronicles FmcQ,W(L,T)

The most specific chronicles are retained

An Inductive Database for Mining Temporal Patterns in Event Sequences

Alexandre Vautier, Marie-Odile Cordier and René Quiniou Irisa - DREAM Project Campus de Beaulieu 35042 RENNES Cedex, FRANCE{Alexandre.Vautier,Marie-Odile.Cordier,Rene.Quiniou}@irisa.fr

More general

More specific

Frequent Minimal Chronicles Search – Fmc SearchFreqW,Q(C,L) ¸ T

Processing a Complex Query

B CBC A

A B BC

L1 :

L2 :

FreqW,Q (C,L1) ¸ T1 Æ FreqW,Q (C,L2) < T2

FmcW,Q(L2,T2)

FmcW,Q(L1,T1)

Chronicle search space

B[-W,W]

A

Fmc SolutionVersion space

Version space computation

Mitchell’s algorithm

Bounds of the version space represent the solution

Only one algorithm is used to compute Fmcs

Frequency of ChroniclesSome Recognition Criteria for Frequency Computation

B CBC A

B CBC

B C

[-2,2]

B 2 instances

Constraints on frequency should satisfy monotonicity or anti-monotonicity properties

3 instances

<Freq(B,L)

¸ Freq(BC,L)

L:

B[-1,3]

[1,5]B[-3,-2]

A

C1

Freq(C,L2) < T2

,: Freq(C,L2) ¸ T2

A

ƒ‚ „Output

Freq(C,L1) ¸ T1

Fmc

A.Vautier